The present invention relates to a method of measuring aberration of a projection optics, and more specifically to a method of measuring aberration of a projection optics, which is designed to measure the aberration by measuring transfer patterns in a photolithography step.
In general, a projection optics is built in various types of devices, for example, an exposure tool, and used in a lithography step in a semiconductor manufacturing process. In these operations, the aberration of the projection lens used, may cause an adverse effect against the acquisition of an accurate projection image.
The deterioration of a projection image is exhibited as, for example, the degradation of its resist image. More specifically, in a lithography step for a trench-type DRAM, a pattern may be transferred asymmetrically when forming a twice hall pattern from a fine deep trench pattern via a projection optics.
The aberration which causes the degradation of a resist image, is presently described while citing "5 aberrations of Suidel", that is, the spherical aberration, astigmatism, coma, field curvature and distortion.
The spherical aberration is the phenomenon that patterns having object planes of difference sizes cause a difference in the position of the transfer image on an image plane. The astigmatism is the phenomenon that the best focus is displaced due to the difference of patterns in their direction. The comma is the phenomenon that a resist profile symmetry is degraded and a placement error is enhanced, which depend on the pattern size, density and feature. The field curvature is the phenomenon that best focuses are displaced from the desired positions in an image plane or an exposure field, the displacements of the best focuses being distributed in a manner.
The word "distortion" means that the image transferred is deformed and displaced from a desired position in an image plane or an exposure field. For the measurement of the aberration, a method which utilizes an interferometer, is conventionally used. Various measurements of the aberration of projection lenses, with use of interferometers, are reported by the makers of the exposure devices.
However, for such a method of measuring the aberration of the projection lens, which uses an interferometer, it is necessary to provide a projection lens within a huge interferometer system. Therefore, once a projection lens is built in the main body of the exposure tool, the aberration thereof cannot be measured. Under these circumstances, there has been a great demand for developing an aberration measurement method which does not require an interferometer, in order to measure the aberration of the projection lens after the projection lens has been built in the main body of the exposure tool, or while operating the exposure tool.
In the meantime, the technique for evaluating the aberration from a projection image has been reported. As an example of measuring the astigmatism, there is a report in "Astigmatism and Field Curvature from Pin-Bars" by Joseph P. Kirk, Proc SPIE 1463, 282-291 (1991). In this document, the best focal difference of line patterns which cross normal to each other on an object plane, obtained on an image plane, is defined as the astigmatism, and it is calculated from the maximum value and the results of measurements of 4 types of patters obtained by setting the orientation degree to 0, 45, 90 and 135 degrees. That is, the astigmatism is the phenomenon that there is a difference in the best focus between two patterns which are orthogonal to each other in direction. However, in the case where the astigmatism is directed to 0.degree. direction (X direction) or 90.degree. direction (Y direction), there will be no difference in the best focus between a pattern directed in 45.degree. direction and a pattern directed in 135.degree. direction. Thus, the astigmatism cannot be measured unless the best focus of each of four types of patterns directed to 0.degree., 45.degree., 90.degree. and 135.degree.. Further, it is known that the relationship between the direction of a pattern and the best focus of its pattern takes a cosine curve theoretically, and therefore the amplitude and the direction of the maximum value obtained when it is curve-fitted with the cosine curve, is expressed as a parameter which characterizes the astigmatism.
In the case of the field curvature, it is measured as a distribution of average best focal points obtained from the above 4 types of patterns, within an exposure field. That is, the field curvature is a phenomenon in which the best focus has a distribution within an exposure field. The best focus position varies depending upon the direction of the pattern due to the astigmatism. Therefore, it is necessary to indicate the field curvature from the average best focus position of 4 patterns directed in the orientation degree to 0, 45, 90 and 135 degrees.
In the case of the coma, periodic patterns on an object, for example, a plurality of line patterns are considered, and it appears as a difference in width between the both ends of the periodic pattern. By measuring the difference in dimension, the aberration of the projection lens can be obtained.
However, in connection with the measurement of the aberration of the projection lens, which is based on the coma, as the size of the object pattern becomes smaller, the reticule manufacturing error and measurement error in the SEM become larger. Therefore, such a technique is not very advantageous for the measurement of the aberration of this sort.
Further, it is conventionally known that the coma displaces the transfer position due to a different in the size of the pattern or density thereof. For example, a 0.3 .mu.m L/S pattern was superimposed on the Si step of a 0.6 .mu.m L/S pattern and then they were exposed. From the superimposing state of these two types of the L/S patters, the coma was measured. (Takashi Saito et al., "Effect if Variable Sigma Aperture on Lens Distortion and its Pattern Size Difference", Proc. SPIE 2725, 414-423 (1996).) (Takashi Saito et al., "Overlay Error of Fine Patterns by Lens Aberration using Modified Illumination" Proc. SPIE 3051, 686-696 (1997).) However, the measuring method discussed in this document requires a great amount of time for preparing a measurement sample, and therefore it is not practical.
Next, in the case where the projection optics is a projection lens, and a specific example where the aberration thereof can be known by measuring the positional error of patterns, which results after the patterns on the photomask are transferred on a substrate, will now be described.
In the case of the coma, periodic patterns on an object, for example, a plurality of line patterns are considered, and it appears as a difference in width between the both ends of the periodic pattern. By measuring the difference in dimension, the aberration of the projection lens can be obtained.
First, the basic structure of the pattern transfer and the displacement of the focal point due to the difference in pattern size, which is the pattern width in the direction that diffraction light occurs, or pitch, which is a distance between patterns repeated, will now be described.
FIG. 1 is a schematic diagram showing how a pattern on a photomask is transferred on a substrate. A pattern 3 on a photomask 2 is illuminated by an illumination system 1, and the image thereof is formed on a substrate 5 via a projection optics. Here, the coherence factor .sigma. is expressed by a ratio between a numerical aperture NAp of the projection optics 4 and a numerical aperture NAi of the illumination system 1.
The light wave diffracted by the pattern 3 formed on the photomask 2 is diffracted at a diffraction angle which is inversely proportional to the size and pitch of the pattern 3. Therefore, when the size and pitch are small, the light wave passes through a light path 7 indicated by two dot chain line, whereas when the size and pitch are large, it passes through a light path 8 indicated by one dot chain line.
As an aberration function 6 of the projection optics 4 is expressed by a curve of a function of the third order or the fifth order, with respect to the pupil radius of the lens, as shown in FIG. 1, since the light path 7 passes through a section where the inclination of the aberration function 6 is large, the image is formed at a point 9 on the substrate 5. On the other hand, the light path 8 passes through a section where the inclination of the aberration function 6 is small, the image is formed at a point 10 on the substrate 5. Thus, there results a difference between the focal positions 9 and 10 due to the difference in the pattern size and pitch.
It is known that the transfer position error due to the size and pitch of the pattern on the photomask causes an asymmetry between before and after the transfer of, for example, patterns of the size, made on both outer sides of five line patterns, as shown in FIG. 2.
The pattern 21 on the photomask before the transfer thereof forms a resist pattern 22 after the transfer. The pattern 21 on the photomask is a pattern which is expressed by a logical product of the periodic pattern 24 and the window pattern 23 including the entire pattern.
Therefore, the resist pattern 22 is also expressed by a logical product of the window pattern 23a after the transfer and the periodic pattern 24a after the transfer. However, the periodic pattern 24 has a size and pitch smaller than those of the window pattern 23, and therefore the transfer positions of the window pattern 23a and the periodic pattern 24a are displaced after the transfer. As a result, a difference is created in the widths L1 and L5 of the line patterns on both side of the resist pattern 22.
In the conventional technique, the difference in the widths of line patters is measured with use of an SEM, and it is used for the measurement of the aberration of a projection optics. However, with this technique, as described before, a strict mask measurement accuracy is required, and therefore when the size of patterns is very much reduced, it becomes difficult to supply photomasks therefor.
Under these circumstances, there has been a great demand of developing an easier measurement method than the conventionally known measurement of the aberration of a projection lens.